### Video Summary:

Consider the graph of
The graph is a parabola with vertex (h,k), and vertical line x = h as axis of symmetry.
The graph opens upward if a > 0 and downward if a < 0. One method to determine the coordinates of the vertex is to complete the square.
Rather than go through the procedure for each individual function, we generalize the result for P(x) = ax² + bx + c. The vertex of the graph of is the
lowest point on the graph if a > 0, or
highest point on the graph if a < 0.
Such points are called extreme points (also extrema, singular: extremum).